Imaging of Extended Objects with Finite Sources

doi:10.1117/3.612961.ch4

Book: Optical Imaging in Projection Microlithography

Author(s): Alfred K. K. Wong

Published: 2005

https://doi.org/10.1117/3.612961.ch4

Author Affiliations +

Abstract

The Fraunhofer diffraction equations derived in the last chapter assume self-luminous point objects. Photomasks used in optical lithography require illumination by light sources that are physically extended. In addition, we must generalize our imaging formulation to consider mask patterns that in reality have finite dimensions. We begin this chapter by studying image formation of a finite object under coherent illumination (by a point source) in which the fields of all object points have a definite phase relationship with one another. We shall find that coherent imaging is characterized by a transfer function that is essentially the point spread function of the imaging system. For a photomask illuminated by a finite source, despite incoherence between source points making up the extended source, vibrations at different object points are correlated due to diffraction of the illumination optics. Analysis under such partially coherent imaging scenarios requires the concept of spatial coherence. Similar to the theory of temporal coherence (quasi-monochromatic light), we need to quantify the correlation of vibrations between two points as a function of their separation and of the characteristics of the light source. We shall learn that partially coherent imaging is characterized by a set of transmission cross-coefficients that is related to the coherent transfer function and the illumination configuration.